Motion fog effect animation

One could create some moving cloudy structures with timeline animation and use that as the basis of a Clipping Mask. 

I agree with S. Gans above that layers is the way to go, with the addition of layer masks. It looks like there are several layers for each square in the image. The way they melt into a new image looks like a Layer mask painted with a soft edge brush, frame by frame to give the feeling of movement and the illusion of the image morphing. 

Here is a link to a tutorial on how to create layer masks: https://helpx.adobe.com/photoshop/how-to/layer-mask.html

Let us know if that helps,

Michelle

This looks like a relatively simple Timeline Frame Animation (https://helpx.adobe.com/photoshop/using/creating-frame-animations.html)
If it was me, I'd use a number of layers, and use the Liquify filter to create variations on the color layer. Then play with transparency on the other layers.... frame by frame... using the layer eyeballs to hide and show layers as you go.
Tedious, but cool!